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Asymptotic properties of the rth power distortion measure associated with quantized k-dimensional random variables are considered. Subject only to a moment condition, it is shown that the infimum over all N level quantizers of the quantity N r'k times the rth power average distortion converges to a finite constant as N + cc

The emerging machine learning technique called support vector machines is proposed as a method for performing nonlinear equalization in communication systems. The support vector machine has the advantage that a smaller number of parameters for the model can be identified in a manner that does not require the extent of prior information or heuristic assumptions that some previous techniques require. Furthermore, the optimization method of a support vector machine is quadratic programming, which is a well-studied and understood mathematical programming technique. Support vector machine simulations are carried out on nonlinear problems previously studied by other researchers using neural networks. This allows initial comparison against other techniques to determine the feasibility of using the proposed method for nonlinear detection. Results show that support vector machines perform as well as neural networks on the nonlinear problems investigated. A method is then proposed to introduce decision feedback processing to support vector machines to address the fact that intersymbol interference (ISI) data generates input vectors having temporal correlation, whereas a standard support vector machine assumes independent input vectors. Presenting the problem from the viewpoint of the pattern space illustrates the utility of a bank of support vector machines. This approach yields a nonlinear processing method that is somewhat different than the nonlinear decision feedback method whereby the linear feedback filter of the decision feedback equalizer is replaced by a Volterra filter. A simulation using a linear system shows that the proposed method performs equally to a conventional decision feedback equalizer for this problem.

We study consensus problems in networked systems with unreliable links. Our contributions are two-fold. First, we derive a family of decentralized consensus algorithms for minimizing a sum of convex functions, fs{z), where each function si only depends on information at one node in the network. Computing the consensus average is a special case in this setting. Then, we con-SQ-UC~ a modified algorithm which is resilient in situations where the channels between nodes act as binary erasure channels. The flexibility and efficacy of our approach is demonstrated through an application of robust estimation.